Summary: Delayed Positive Feedback Can Stabilize Oscillatory
Systems
C. Abdallah, P. Dorato, and J. Benitez-Read
Department of EECE
University of New Mexico
Albuquerque, NM 87131, USA
and
R. Byrne
Sandia National Laboratories, Department 9616
Albuquerque, NM 87185
March 21, 2003
ABSTRACT
This paper expands on a method proposed in [1] for stabilizing oscillatory systems with
positive, delayed feedback. The closed-loop system obtained is shown (using the Nyquist
criterion) to be stable for a range of delays.
1 Introduction
The stabilization of ocillatory systems finds applications in robotics [2] and flexible structures
[1]. A simple example of an oscillatory system is given by the second-order system
¨y + w2
0y = u (1)